Weak convergence of subordinators to extremal processes

For certain subordinators (Xt)t≥0 it is shown that the process (−tlogXts)s>0 tends to an extremal process (η̂s)s>0 in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that (z∧(−tlogXts))s≥0 converges weakly to (z∧η̂s)s≥0 in D[0,∞), the space of càdlàg functions equipped with Skorohod’s J1 metric.

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Year of publication:	2013
Authors:	Kella, Offer ; Löpker, Andreas
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 123.2013, 8, p. 3122-3131
Publisher:	Elsevier
Subject:	Lévy process \| Subordinator \| Extremal process \| Small-time convergence

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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